e. S(z) = sin(z) f. S(z) = sin(z) 8. E(z) = e*-1 h. E(z) = e 1. Find all periodic points for each of the following maps and classify them as attracting, repelling, or neither. Sketch the phase portraits. a. f(z) = z-z2 b. f(2) = 2(z - z) c. f(z) = z-2 d. f(z) = 2 - z i. A(z) = arctan z jA(z) = arctan z

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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a, d , and h only

e. S(z) = sin(z)
f. S(z) = sin(z)
8. E(z) = e-1
h. E(z) = e²
1. Find all periodic points for each of the following maps and classify them
as attracting, repelling, or neither. Sketch the phase portraits.
%3D
%3D
a. f(z) = z -
b. f(z) = 2(z- z²)
c. f(z) = z' -
d. f(z) = z - z
%3D
%3D
i. A(z) = arctan z
%3D
j. A(z) = arctan z
%3D
Transcribed Image Text:e. S(z) = sin(z) f. S(z) = sin(z) 8. E(z) = e-1 h. E(z) = e² 1. Find all periodic points for each of the following maps and classify them as attracting, repelling, or neither. Sketch the phase portraits. %3D %3D a. f(z) = z - b. f(z) = 2(z- z²) c. f(z) = z' - d. f(z) = z - z %3D %3D i. A(z) = arctan z %3D j. A(z) = arctan z %3D
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